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The long-time CEO of Wells Fargo agreed on Tuesday to forfeit $41 million (NZ$56.3m) in performance pay three weeks after the bank acknowledged that for at least five years thousands of low-level employees allegedly set up sham accounts to meet sales quotas.

The San Francisco-based bank has repeatedly apologized for the scheme and said it had fired 5,300 employees for bad behavior and put in place more stringent internal controls.

But that hasn't been enough for lawmakers who have been pushing for the company's top leaders to give back the millions in bonuses they earned while the misconduct was occurring.

The independent directors of the Wells Fargo board announced Tuesday that they were launching an investigation into the Wells Fargo's retail business.

"We are deeply concerned by these matters, and we are committed to ensuring that all aspects of the Company's business are conducted with integrity, transparency, and oversight," Stephen Sanger, the lead independent director, said in a statement.

John Stumpf, the chief executive, will forfeit unvested stock awards currently worth about $41m (NZ$56.3) will not receive a salary while the investigation is ongoing and will not be eligible for a 2016 bonus, the committee said in a statement.

Carrie Tolstedt, the former head of Wells Fargo community bank unit, where the misconduct took place, will give up $19m (NZ$26m) in unvested stock awards and not be eligible for a 2016 bonus. Tolstedt had announced her retirement in July, but had initially planned to stay at the bank until the end of the year.

Both Stumpf and Tolstedt still have millions in stock and other compensation at Wells Fargo. But this action by the bank's board is, by far, the most aggressive and public effort by a financial firm since the 2008 financial crisis to show that top executives will be held responsible for misdeeds.

In early September, Wells Fargo was fined $185m (NZ$254m) by regulators after it discovered that thousands of employees were setting up unauthorized accounts, from credit cards to checking accounts, that customers didn't ask for. In some cases, the customer was charged various fees for accounts they didn't know existed.

The case has sparked a national outcry with lawmakers pummeling Stumpf before the Senate Banking Committee last week, with one even calling on him to resign. He is to be the only witness before the House Financial Services Committee and this move could help head off some of the inevitable recrimination from lawmakers.